I can feel it too. I wasn't always able to do that, but after the changes kicked in some years back, I started feeling the energies of stones.
Yes, but they're stronger when somebody else has been holding them. I have a healer friend who carries stones with her. When I hold them I feel her energy, which is powerful and radiant. But in general, I don't feel much when I hold stones if they've just been sitting there on a shelf.
I took a 101 Crystal course and while there, we were told to pick out a crystal that called to us. Then we all sat down and placed it in our left hands while we grounded ourselves. I felt nothing. I bought the crystal anyway because it was calling me. When at home, I sat down, held it in my left hand, then placed my right hand over it. THAT'S when I felt it! I got tingles in my hands. It's the same tingle I get when getting a tarot reading or working with a fellow empath. It's pretty cool!